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SRS Relative pair #487521671
details
property
value
status
complete
benchmark
rel06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Zantema_06_relative
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
12.2839560509 seconds
cpu usage
44.717409068
max memory
4.6093312E9
stage attributes
key
value
output-size
19854
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 75 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 30 ms] (4) RelTRS (5) FlatCCProof [EQUIVALENT, 0 ms] (6) RelTRS (7) RootLabelingProof [EQUIVALENT, 1 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 15 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 12 ms] (12) RelTRS (13) RelTRSRRRProof [EQUIVALENT, 111 ms] (14) RelTRS (15) RelTRSRRRProof [EQUIVALENT, 143 ms] (16) RelTRS (17) RelTRSRRRProof [EQUIVALENT, 3 ms] (18) RelTRS (19) RelTRSRRRProof [EQUIVALENT, 0 ms] (20) RelTRS (21) RelTRSRRRProof [EQUIVALENT, 28 ms] (22) RelTRS (23) RelTRSRRRProof [EQUIVALENT, 296 ms] (24) RelTRS (25) RIsEmptyProof [EQUIVALENT, 0 ms] (26) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(x1) -> b(c(x1)) a(b(x1)) -> b(a(x1)) a(c(x1)) -> c(a(x1)) The relative TRS consists of the following S rules: d(c(x1)) -> d(a(x1)) d(a(x1)) -> d(c(b(x1))) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(a(x_1)) = [[1], [1]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(b(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(c(x_1)) = [[0], [2]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(d(x_1)) = [[0], [0]] + [[2, 2], [0, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: a(x1) -> b(c(x1)) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(b(x1)) -> b(a(x1)) a(c(x1)) -> c(a(x1))
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